What was already known
Daskalakis–Golowich had a weaker bound after a Ramsey step. Conant and Terry already had the uniform induction and key tree lemmas before using ChatGPT.
AI involvement
After identifying the obstacle and supplying a draft with the induction and rough two-case structure, the human authors asked ChatGPT for a proof. They report that it generated the argument now used for tight extraction. This is central AI input within a human-designed scheme, supporting AI-centered rather than AI-led or autonomous.
The acknowledgments credit ChatGPT with the new tight-extraction argument, while stating that the authors supplied the scheme, obstacles, earlier lemmas, and final rewrite.
Importance
Improves the quantitative tight-extraction bound in learning-theoretic combinatorics.
Limitations
The paper’s double-exponential dual sequential fat-shattering corollary follows from the authors’ earlier human proof and is not credited to the model.
Technical verification
The two named human authors expressly report careful checking of all ChatGPT-generated proofs, including the Theorem 1.14 argument, and thorough rewriting. This is source-reported human proof checking, not a machine formalization or independent reproduction.
Formal checking
Careful human checking and complete rewriting of generated proofs and examples
- Checker
- G. Conant and C. Terry, paper authors
- Scope
- ChatGPT-generated tight-threshold extraction argument used for Theorem 1.14
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors explain how their induction is elaborated to obtain a proto-ladder and fully tight ladder without the older multicolored Ramsey loss, and they rewrote the generated argument.
Correction and publication history
Improves the quantitative tight-extraction bound in learning-theoretic combinatorics.
Read this published revision